The following are examples of wavelength dispersion compensation in an optical waveguide structure which does not consider polarization dependence.
An element having a plurality of Bragg grating elements in which the cycle changes spatially such that wavelength dispersion is compensated in a plurality of wavelength channels is disclosed in Patent document 1 (U.S. Pat. No. 6,865,319) as a dispersion compensation element which has a Bragg grating pattern on the waveguide. Moreover, Patent document 1 also discloses that a refractive index distribution n (z) of the Bragg grating which is formed by a plurality of elements extending in the direction of the optical axis of the waveguide also shows sinusoidal changes as shown in the following formula (wherein z is the position of a point on the light propagation axis).
                    [                  Expression          ⁢                                          ⁢          1                ]                                                                      n          ⁡                      (            z            )                          =                                            n              eff                        ⁡                          (              z              )                                +                                    ∑                              i                =                1                            m                        ⁢                          Δ              ⁢                                                          ⁢                                                n                  i                                ⁡                                  (                  z                  )                                            ⁢                              sin                ⁡                                  (                                                                                    ∫                        0                        z                                            ⁢                                                                                                    2                            ⁢                            π                                                                                                              p                              i                                                        ⁡                                                          (                                                              z                                ′                                                            )                                                                                                      ⁢                                                                                                  ⁢                                                  ⅆ                                                      z                            ′                                                                                                                +                                          ϕ                      i                                                        )                                                                                        (                  Formula          ⁢                                          ⁢          1                )            
In a sine wave component which corresponds to the Bragg grating pattern of each wavelength channel, the pitch (local cycle) p, gradually changes (i.e., chirps) together with z. In FIG. 3 of Patent document 1, the pitch chirps in a direction in which it decreases in response to increases in z. In addition, an origin phase φi changes discretely in each grating element i. As in the above described formula, the Bragg grating pattern which corresponds to each channel is defined independently, and a Bragg grating pattern is formed by superimposing these patterns. In Patent document 1, a case is illustrated in which a Bragg grating pattern is formed in an optical fiber.
In Patent document 2 (U.S. Pat. No. 6,707,967), a wavelength dispersion compensation element is described in which a Bragg grating having one cycle is formed on the waveguide path, and a sampling structure is formed on the waveguide path which is superimposed on this Bragg grating, so that wavelength dispersion compensation is performed in a plurality of wavelength channels. The sampling structure is formed by a pattern that has undergone phase sampling in one cycle which is longer than the cycle of the Bragg grating. Each cycle of the phase sampling is divided into a plurality of spatial areas in a direction along the optical axis of the waveguide, and the phase of the Bragg grating changes discontinuously at a boundary where mutually adjacent spatial areas are in contact with each other. As is shown in FIG. 1A through FIG. 1D of Patent document 2, there are no discontinuous phase changes within a single spatial area.
In Patent document 3 (Japanese Patent No. 3262312), a two-input and two-output light dispersion equalizer is described that performs wavelength dispersion compensation. The light dispersion equalizer has a structure as a basic component element in which two optical waveguides are coupled by a plurality of directional couplers, the optical path lengths of two waveguides in a region sandwiched by two adjacent directional couplers are mutually different, and a phase controller is provided in at least one of the two waveguides. In this document, a device is illustrated that compensates a dispersion slope using these waveguides, and an element that compensates wavelength dispersion is provided in an optical input section. Furthermore, this document also described that increasing the number of stages formed by connecting the aforementioned basic component elements in series, in order to increase the compensation effect.
In Patent document 4 (Japanese Patent No. 3415267), a design method for an optical signal processor is described in which a structure provided with a directional coupler having an amplitude coupling ratio ranging from a positive value to a negative value on one side of two waveguides having an optical path difference is used as a basic component element, and these basic component elements are combined in a series so as to form a two-input and two-output optical circuit with no feedback (namely, no reflection). In this design technique, the structure of the optical circuit is decided by expressing the characteristics of the optical circuit using a two-row two-column unitary matrix, imparting the desired output characteristics of the cross-port, and calculating amplitude parameters of the directional coupler in which the amplitude parameters are unknown parameters of the optical circuit. An example of the design of a wavelength dispersion compensation element that is based on this design method is given in the Examples.
In Patent document 5 (Japanese Patent No. 3917170), a broadband wavelength dispersion compensation element that employs a high refractive index waveguide that uses photonic crystals is described, and in which wavelength dispersion compensation is performed by a transmission type of optical waveguide structure. The coding of the wavelength dispersion can be changed.
In Non-patent document 1 (“Phase-Only Sampled Fiber Bragg Gratings for High-Channel-Count Chromatic Dispersion Compensation” H. Li, Y. Sheng, Y. Li and J. E. Rothenberg, Journal of Lightwave Technology, Vol. 21, No. 9, September 2003, pp. 2074-2083), an actual fiber Bragg grating wavelength dispersion compensation element is prepared using a design technique similar to that of Patent document 2, and the result of this is described. Firstly, a Bragg grating pattern of a single channel in a center wavelength is designed using the information in Non-patent document 2 (“An Efficient Inverse Scattering Algorithm for the Design of Nonuniform Fiber Bragg Gratings” R. Feced, M. N. Zervas and M. A. Muriel, IEEE Journal of Quantum Electronics, Vol. 35, No. 8, 1999, pp. 1105-1115). The grating pattern is derived using an inverse scattering solution from the spectrum characteristics of the desired reflection and wavelength dispersion. However, in the fiber Bragg grating, because there are limits to the range over which the refractive index can be changed in order to manufacture a grating pattern, an operation in which the aforementioned spectrum characteristics are apodized by undergoing an inverse Fourier transform is also carried out so that these limits are not exceeded. As a result of this, a pattern is obtained in which the pitch of the Bragg grating changes continuously together with the position. Thereafter, Bragg grating patterns are designed using phase sampling for a plurality of channels. In a fiber Bragg grating, because there are limits on the range of refractive index change, phase sampling is effective.
In Non-patent document 2, an algorithm of a solution for the problem of inverse scattering which is based on layer peeling solution is described, and an example of the analysis of a wavelength dispersion compensation element that employs a fiber Bragg grating is illustrated.
In Non-patent document 3 (“Integrated-Optic Dispersion Compensator that uses Chirped Gratings” C. J. Brooks, G. L. Vossler and K. A. Winick, Optics Letters, Vol. 20, No. 4, 1995, pp. 368-370), a wavelength dispersion compensation element that employs a chirped Bragg grating waveguide on a substrate is described. In this wavelength dispersion compensation element, a rectangular optical waveguide core is formed by silver ion exchange on a silica glass substrate, and a Bragg grating pattern is formed in silica cladding on a top portion of the core. Because the grating pitch is gradually changed, the propagation axis of the core of the optical waveguide is bent. Laser light pulses having a wavelength of 800 nm are irradiated thereon so that 58 ps/nm is obtained for an optical waveguide having a 7 mm grating length. Using a grating having a length of 50 mm, it is possible to perform wavelength dispersion compensation for an optical fiber equivalent to 50 km at a wavelength of 1550 nm.
In FIGS. 1 (a) and (b) and FIG. 3 (a) of Non-patent document 4 (“Guiding and Confining Light in Void Nanostructure” Vilson R. Almeida et. al, Optics Letters, Vol. 29, No. 11, 2004, pp. 1209-1211), a slot-type optical waveguide element is described that has a structure in which light is confined in silica glass (having a refractive index of 1.46, a width of 50 nm and a height of 300 nm) in a center gap region that is sandwiched between rectangular silicon (i.e., between two locations that each have a refractive index of 3.48, a width of 180 nm and a height of 300 nm).